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I remember reading a long time ago, the story of a student taking R. Feynman for responsible of her (I think it was a woman, not sure though) fail at an exam of physics because what was written in her textbook was false and him to tell her back that she should have checked with other textbooks. In other words, it's not because you are R. Feynman that typos are impossible.


Recently, I read for the first time the chapters on thermodynamics and after all corrections that may have been done I am still surprised to read equations written as follow:

$$dQ + dW = dU \tag 1$$

$$ \Delta U = \Delta Q + \Delta W \tag 2$$

reference (09/18/2019)


Is that a pure error from himself, who, as little as I know him through his lectures, was really precise on details, or was the notations $\delta Q$ and $\delta W$ later introduced to clearly make the distinction between exact and inexact differentials?

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    $\begingroup$ He probably didn't bother to distinguish the two. Not everybody does. $\endgroup$
    – knzhou
    Commented Sep 18, 2019 at 0:39
  • $\begingroup$ ...which is incredibly confusing. In fact, the terms "exact differential" and "inexact differential" are themselves confusing. The mathematics community has a reasonable and consistent phraseology about this stuff that physicists should just use instead of inventing half-baked confusing pseudo-notation :-) $\endgroup$
    – DanielSank
    Commented Sep 18, 2019 at 6:02
  • $\begingroup$ Wow, I'm really surprised that it appears in Feynman's book. $dQ$ vs $\delta Q$ might be a bit of a personal taste, but given that heat and work aren't state functions, it's quite simply non-sensical to write a $\Delta$ in front of $Q$ or $W$. It's pretty hard to define $Q_2 - Q_1$ since neither $Q_1$ nor $Q_2$ are defined. My cognitive dissonance is strong on this one : I habe the utmost respect for Feynman as a physicist and teacher. And I've always read $\Delta W$ as a clear notation of "the writer doesn't understand thermodynamics and shouldn't write about it". $\endgroup$ Commented Dec 25, 2022 at 1:32

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There is no standardization for the notation of exact versus inexact differentials. In fact, I do not think I have ever seen the $\delta Q$ notation that you seemed to be expecting. Many authors have tried to introduce specific notations, but none of them has been uniformly adopted, and plenty of writers (such as Feynman) continue to write $dQ$, even though they know that $Q$ is not a state function. Moreover, other notations for inexact (some authors prefer "non-exact") differentials include $d\!\!\!\!\!\not\,Q$, and $\dot{Q}\,dt$. The last one, with $\dot{Q}$, seems to me to be potentially even more confusing than bare $dQ$, but it nonetheless gets a fair amount of use, particularly by engineers.

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    $\begingroup$ Actually, a guy who knew thermodynamics quite well (Planck), in his textbook, wrote the first principle as $d U = Q + W$, which is probably the best ever notation. $\endgroup$ Commented Sep 18, 2019 at 14:22

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